Systems and methods for converting discrete wavelets to tensor fields and using neural networks to process tensor fields

ABSTRACT

The present disclosure relates to systems and methods for detecting and identifying anomalies within a discrete wavelet database. In one implementation, the system may include one or more memories storing instructions and one or more processors configured to execute the instructions. The instructions may include instructions to receive a new wavelet, convert the net transaction to a wavelet, convert the wavelet to a tensor using an exponential smoothing average, calculate a difference field between the tensor and a field having one or more previous transactions represented as tensors, perform a weighted summation of the difference field to produce a difference vector, apply one or more models to the difference vector to determine a likelihood of the new wavelet representing an anomaly, and add the new wavelet to the field when the likelihood is below a threshold.

TECHNICAL FIELD

The present disclosure relates generally to the field of neuralnetworks. More specifically, and without limitation, this disclosurerelates to systems and methods for using neural networks to processdiscrete tensor fields.

BACKGROUND

Extant methods of risk detection rely on rule-based determinations,decision trees, or artificial neural networks. However, each extantmethod suffers from shortfalls. For example, rule-based determinationstend to have high error rates, which are inconvenient for financialmarkets. Although decision trees may have lower error rates thanrule-based determinations, they often rely on manual verification alongone or more branches, as well as increasing complexity and processingresources. Finally, artificial neural networks fail to recognize manypatterns and exponentially increase resource drain as the number ofhidden neuron layers increases linearly.

Moreover, extant rules, trees, and neural networks must be implementedseparately. This both reduces processing efficiency and requires furtherresource drain and algorithmic complexity to handle disparate resultsfrom the rules, trees, and networks.

Additionally inefficiencies inhere in the storage of discrete datarepresenting transactions. This discrete data is generally stored in arelational database or a graph database. The former relies onresource-costly searches and concatenations while the latter relies onexponentially costly nodal traversals.

SUMMARY

In view of the foregoing, embodiments of the present disclosure providesystems and methods for constructing and using wavelet databases topredict risk through neural networks.

As used herein, “database” refers to a “data space,” which is a tertiarydatabase that uses in-process RAM dictionaries, a shared memory datacache, a multi-process/multi-server object cache, and one or more commondatabases (e.g., a Structured Query Language (SQL) database) and/orBinary Large Objects (BLOBs).

According to an example embodiment of the present disclosure, a systemfor detecting anomalies within a database comprising discrete waveletsmay comprise one or more memories storing instructions and one or moreprocessors configured to execute the instructions. The instructions mayinclude instructions to receive a new wavelet, convert the wavelet to atensor using an exponential smoothing average, calculate a differencefield between the tensor and a field having one or more previouswavelets represented as tensors, perform a weighted summation of thedifference field to produce a difference vector, apply one or moremodels to the difference vector to determine a likelihood of the newwavelet representing an anomaly, and add the new wavelet to the fieldwhen the likelihood is below a threshold.

In another embodiment, a system for training a deep field network todetect anomalies within a database comprising discrete wavelets maycomprise one or more memories storing instructions and one or moreprocessors configured to execute the instructions. The instructions mayinclude instructions to receive a plurality of transactions, converteach transaction to a corresponding wavelet, group the plurality ofwavelets and corresponding tensors by coefficients included in thewavelets, train a neural network for each group independently of othergroups, and integrate the neural networks into a deep field network.

In another embodiment, a system for authorizing a transaction usingcascading discrete wavelets may comprise one or more memories storinginstructions and one or more processors configured to execute theinstructions. The instructions may include instructions to receive a newtransaction, convert the new transaction to a wavelet, convert thewavelet to a tensor using an exponential smoothing average, calculate adifference field between the tensor and a field having one or moreprevious transactions represented as tensors, perform a weightedsummation of the difference field to produce a difference vector, applyone or more models to the difference vector to determine a likelihood ofthe transaction being high risk, and authorize the new transaction whenthe likelihood is below a threshold.

Any of the alternate embodiments for disclosed systems for indexing andrestructuring a headshot database for a user may apply to disclosednon-transitory computer-readable media storing instructions for indexingand restructuring a headshot database for a user.

It is to be understood that the foregoing general description and thefollowing detailed description are exemplary and explanatory only, andare not restrictive of the disclosed embodiments.

Further, by employing the unconventional training disclosed herein, adeep field network may be trained to function with greater efficiencyand accuracy than extant neural networks as well as trained to operateon a wavelet database rather than a relational or graph database. Inaddition, by employing the unconventional deep field network disclosedherein, more accurate and efficient detection of anomalies may beperformed than by using extant rule-based systems, decision trees, orneural networks.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which comprise a part of this specification,illustrate several embodiments and, together with the description, serveto explain the principles disclosed herein. In the drawings:

FIG. 1 is a diagram of a wavelet, according to an exemplary embodimentof the present disclosure.

FIG. 2A is a block diagram of a filter bank, according to an exemplaryembodiment of the present disclosure.

FIG. 2B is a graphical representation of the exemplary filter bank ofFIG. 2A.

FIG. 3 is a diagram of a convolutional-accumulator, according to anexemplary embodiment of the present disclosure.

FIG. 4 is a graphical representation of exponential smoothingcoefficients, according to an exemplary embodiment of the presentdisclosure.

FIG. 5 is a block diagram of tensor extrapolation from wavelets,according to an exemplary embodiment of the present disclosure.

FIG. 6 is a graphical representation of a manifold, according to anexemplary embodiment of the present disclosure.

FIG. 7 is a graphical representation of an atlas mapping a manifold to alinear space, according to an exemplary embodiment of the presentdisclosure.

FIG. 8 is a diagram of a Galois connection, according to an exemplaryembodiment of the present disclosure.

FIG. 9 is a diagram of an exemplary artificial neural network.

FIG. 10A is a block diagram of an exemplary system for detectinganomalies within a database comprising discrete wavelets, according toan exemplary embodiment of the present disclosure.

FIG. 10B is a block diagram of another exemplary system for detectinganomalies within a database comprising discrete wavelets, according toan exemplary embodiment of the present disclosure.

FIG. 10C is a block diagram of an exemplary workflow for detecting highrisk transactions using a database comprising discrete wavelets,according to an exemplary embodiment of the present disclosure.

FIG. 10D is a block diagram of an exemplary workflow for constructingand using a database comprising discrete wavelets, according to anexemplary embodiment of the present disclosure.

FIG. 11 is a diagram of an example of training a deep field network todetect anomalies within a database comprising discrete wavelets,according to an exemplary embodiment of the present disclosure.

FIG. 12 is a flowchart of an exemplary method for detecting anomalieswithin a database comprising discrete wavelets, according to anexemplary embodiment of the present disclosure.

FIG. 13 is a flowchart of an exemplary method for training a deep fieldnetwork to detect anomalies within a database comprising discretewavelets, according to an exemplary embodiment of the presentdisclosure.

FIG. 14 is a flowchart of an exemplary method for authorizing atransaction using cascading discrete wavelets, according to an exemplaryembodiment of the present disclosure.

FIG. 15 is a block diagram of an exemplary computing device with whichthe systems, methods, and apparatuses of the present disclosure may beimplemented.

DETAILED DESCRIPTION

The disclosed embodiments relate to systems and methods for detectinganomalies within a database comprising discrete wavelets, training adeep field network to detect anomalies within a database comprisingdiscrete wavelets, and authorizing a transaction using cascadingdiscrete wavelets. Embodiments of the present disclosure may beimplemented using a general-purpose computer. Alternatively, aspecial-purpose computer may be built according to embodiments of thepresent disclosure using suitable logic elements.

As used herein, “deep field network” refers to one or more trainedalgorithms integrated into a prediction schema. In some embodiments,deep field networks may be applied to a multi-nodal manifold converteddifferential field, e.g., determined based on the difference between awavelet converted to a tensor and a field of existing (e.g., previous)tensors.

Disclosed embodiments allow for efficient and accurate detection ofanomalies within a wavelet database. Additionally, embodiments of thepresent disclosure allow for efficient and accurate authorization oftransactions using a wavelet database. Furthermore, embodiments of thepresent disclosure provide for greater flexibility and accuracy thanextant anomaly detection techniques, such as rule-based determinations,decision trees, and neural networks.

According to an aspect of the present disclosure, a processor mayreceive a new wavelet. As used herein, the term “wavelet” refers to anydata that may be represented as a brief oscillation. The wavelet neednot be received in the form of an oscillation but may be represented inany appropriate form (e.g., an array, a digital signal, or the like).The wavelet may be received from one or more memories (e.g., a volatilememory such as a random access memory (RAM) and/or a non-volatile memorysuch as a hard disk) and/or across one or more computer networks (e.g.,the Internet, a local area network (LAN), or the like). Alternatively,the processor may receive data and convert the data into a wavelet. Forexample, the processor may receive a transaction having associatedproperties (such as time, location, merchant, amount, etc.) and mayconvert the transaction into a wavelet or into an array or other formatthat represents a wavelet.

The processor may convert the wavelet to a tensor. For example, a tensormay represent an array that satisfies one or more mathematical rules(for example, a tensor may be a multi-dimensional array with respect toone or more valid bases of a multi-dimensional space).

In some embodiments, the processor may convert the wavelet to a tensorusing a moving average. For example, a simple moving average, acumulative moving average, a weighted moving average, or the like, maybe used to convert the wavelet to a tensor. In certain aspects, theprocessor may convert the wavelet to a tensor using an exponentialsmoothing average. By using an exponential smoothing average, thenatural base e may be incorporated into the smoothing. Because erepresents the limit of compound interest, the smoothed wavelet may beeasier to identify as anomalous within a financial market. Accordingly,the processor may perform a discrete wavelet transform with anexponential smoothing average accumulator to transform the receivedwavelet into a tensor.

The processor may calculate a difference field between the tensor and afield having one or more previous wavelets represented as tensors. Forexample, the field may have been previously constructed as explainedabove. That is, the processor may perform a discrete wavelet transformwith an exponential smoothing average accumulator to transform the oneor more previous wavelets into tensors. The processor may then obtainthe field by mapping the tensors onto a manifold (e.g., a differentialmanifold). One or more atlases may be used in order to do so.Alternatively, the processor may receive the tensors (e.g., from one ormore memories and/or over one or more computer networks) and constructthe field therefrom or may receive the field directly (e.g., from one ormore memories and/or over one or more computer networks).

In some embodiments, the difference field may represent a tensor productof fields (i.e., between a field having only the tensor and the fieldhaving the one or more previous wavelets represented as tensors).Accordingly, the difference field may represent a Galois connectionbetween the tensor and the field.

The processor may perform a weighted summation of the difference fieldto produce a difference vector. For example, the coefficient weights maybe derived from training of one or more particular models. For example,the processor may apply a variety of models in the weighting, such asmodels trained for particular identifiers (e.g., particular accounts,particular persons, particular merchants, particular institutions,etc.), particular times (e.g., time of day, time of year, etc.),particular locations (e.g., particular country, particular city,particular postal code, etc.), or the like.

Additionally or alternatively, the summation may include a notch filter.Accordingly, particular frequencies may be filtered out during thesummation. For example, the processor may apply one or more particularmodels to determine which particular frequencies to filter out. The oneor more filter models may be the same models as the one or moreweighting models or may be different models.

In some embodiments, an absolute or a squaring function may be applied.Alternatively, the weighted summation may produce a directionaldifference vector. Accordingly, the difference vector may include adirection of the difference as well as a magnitude of the difference.This additional information may improve accuracy of the anomalydetection. For example, a large difference vector pointing in anexpected direction may be less anomalous than a small difference vectorpointing in an unexpected direction.

The processor may apply one or more models to the difference vector todetermine a likelihood of the new wavelet representing an anomaly. Forexample, the one or more likelihood models may be the same models as theone or more filter models and/or the one or more weighting models or maybe different models. In embodiments having direction as well asmagnitude, the one or more models may use the magnitude and direction ofthe difference vector to determine the likelihood. As used herein,“likelihood” may refer to a percentage (e.g., 50%, 60%, 70%, etc.), aset of odds (e.g., 1:3, 1 in 5, etc.), a score (e.g., 1 out of 5, 5.6out of 10.0, etc.), an indicator (e.g., “not likely,” “likely,” “verylikely,” etc.), or the like.

Based on the likelihood, the processor may either add the new wavelet tothe field or reject the new wavelet. For example, the processor may addthe new wavelet to the field when the likelihood is below a threshold.If the processor rejects the new wavelet, the processor may send anotification to such effect. For example, the processor may send arejection signal or a message indicating the likelihood and/or a reason(e.g., based on the one or more models) for rejection. The processor maysend the notification to one or more parties associated with the newwavelet (e.g., a financial institution, an individual, a merchant, orthe like) and/or to one or more computer systems from which the newwavelet was received (e.g., a personal computer such as a desktopcomputer or mobile phone, a point-of-service system, a financialprocessing server, a credit bureau server, or the like).

According to a second aspect of the present disclosure, a processor mayreceive a plurality of transactions. As used herein, the term“transactions” refers to any data including an indication of an amountof currency or commodity that is transferred between parties. Thetransactions need not be received in any particular format but may berepresented in any appropriate form such as arrays, digital signals, orthe like. The transactions may be received from one or more memories(e.g., a volatile memory such as a random access memory (RAM) and/or anon-volatile memory such as a hard disk) and/or across one or morecomputer networks (e.g., the Internet, a local area network (LAN), orthe like). Alternatively, the processor may receive raw data and convertthe data into a format representing a transaction. For example, theprocessor may receive a data with time, location, party identifiers,amount, and the like and may convert this data into a single bundlerepresenting a transaction.

The processor may convert each transaction to a corresponding wavelet.For example, as explained above, the processor may receive a transactionhaving associated properties (such as time, location, merchant, amount,etc.) and may convert the transaction (along with its associatedproperties) into a wavelet or into an array or other format thatrepresents a wavelet.

The processor may group the plurality of wavelets and correspondingtensors by coefficients included in the wavelets. For example, thecorresponding tensors may be determined using an exponential smoothingaverage. That is, the processor may perform a discrete wavelet transformwith an exponential smoothing average accumulator to transform thewavelets into corresponding tensors.

Because each tensor includes coefficients for each base in the set ofbases representing a corresponding multi-dimensional space in which thetensor may be represented, the processor may group the tensors (andtherefore, the corresponding wavelets) by these coefficients. Becausethe coefficients depend on the bases selected (which must satisfy one ormore mathematical rules in order to form a mathematically consistentmulti-dimensional space), the processor may generate a plurality ofgroups of coefficients and, thus, a plurality of groupings of thetensors (with the corresponding wavelets). For example, the processormay select bases depending on which factors are most heavily weighted inone or more models and then perform a plurality of groupings, each for aparticular model (or set of models) having factors corresponding to thebases used to determine the corresponding grouping.

The processor may train a neural network for each group independently ofother groups. Although “neural network” usually refers to a traditionalartificial neural network as depicted, for example, in FIG. 9, theprocessor here may train any model (e.g., the models discussed abovewith respect to the groupings) that produces a likelihood of aparticular tensor being anomalistic within a group. By training eachgroup independently, the processor may develop specialized models thatare orders of magnitude greater in number (and, therefore, accuracy)than extant neural networks. For example, the processor may developthousands (or even millions) of models without requiring exponentiallymore resources than used to construct a single artificial neuralnetwork.

The processor may integrate the neural networks into a deep fieldnetwork. For example, the models may be combined into a largerpredictive scheme. In one particular example, the models may be combinedsuch that when a new tensor is convolved (or otherwise combined with themodels), the model trained on the group (or groups) having the mostsimilar coefficients will be amplified while other models (e.g., trainedon groups with less similar coefficients) will be minimized.

According to a third aspect of the present disclosure, a processor mayreceive a new transaction. For example, as explained above, the term“transaction” refers to any data including an indication of an amount ofcurrency or commodity that is transferred between parties. Thetransaction need not be received in any particular format but may berepresented in any appropriate form such as arrays, digital signals, orthe like. The transaction may be received from one or more memories(e.g., a volatile memory such as a random access memory (RAM) and/or anon-volatile memory such as a hard disk) and/or across one or morecomputer networks (e.g., the Internet, a local area network (LAN), orthe like). Alternatively, the processor may receive raw data and convertthe data into a format representing a transaction. For example, theprocessor may receive a data with time, location, party identifiers,amount, and the like and may convert this data into a single bundlerepresenting a transaction.

The processor may convert the new transaction to a wavelet. For example,as explained above, the new transaction may have associated properties(such as time, location, merchant, amount, etc.), and the processor mayconvert the new transaction (along with its associated properties) intoa wavelet or into an array or other format that represents a wavelet.

The processor may convert the wavelet to a tensor using an exponentialsmoothing average. For example, as explained above, the processor mayperform a discrete wavelet transform with an exponential smoothingaverage accumulator to transform the wavelet into a correspondingtensor.

The processor may calculate a difference field between the tensor and afield having one or more previous transactions represented as tensors.For example, as explained above, the processor may have performed adiscrete wavelet transform with an exponential smoothing averageaccumulator to transform the one or more previous transactions intotensors. The processor may then obtain the field by mapping the tensorsonto a manifold (e.g., a differential manifold). One or more atlases maybe used to map the tensors onto the manifold. Alternatively, theprocessor may receive the tensors (e.g., from one or more memoriesand/or over one or more computer networks) and construct the fieldtherefrom or may receive the field directly (e.g., from one or morememories and/or over one or more computer networks).

The processor may perform a weighted summation of the difference fieldto produce a difference vector. For example, as explained above, thecoefficient weights may be derived from training of one or moreparticular models. For example, the processor may apply a variety ofmodels in the weighting, such as models trained for particularidentifiers (e.g., particular accounts, particular persons, particularmerchants, particular institutions, etc.), particular times (e.g., timeof day, time of year, etc.), particular locations (e.g., particularcountry, particular city, particular postal code, etc.), or the like.

Additionally or alternatively, the summation may include a notch filter.Accordingly, particular frequencies may be filtered out during thesummation. For example, the processor may apply one or more particularmodels to determine which particular frequencies to filter out. The oneor more filter models may be the same models as the one or moreweighting models or may be different models.

The processor may apply one or more models to the difference vector todetermine a likelihood of the transaction being high risk. For example,the one or more likelihood models may be the same models as the one ormore filter models and/or the one or more weighting models or may bedifferent models. In embodiments having direction as well as magnitude,the one or more models may use the magnitude and direction of thedifference vector to determine the likelihood. As used herein,“likelihood” may refer to a percentage (e.g., 50%, 60%, 70%, etc.), aset of odds (e.g., 1:3, 1 in 5, etc.), a score (e.g., 1 out of 5, 5.6out of 10.0, etc.), an indicator (e.g., “not likely,” “likely,” “verylikely,” etc.), or the like.

As used herein, “risk” refers to any quantification of the probabilityof a transaction being lost (e.g., via automatic decline, insolvency ofthe purchaser, fraudulency, or the like). Accordingly, “high risk”refers to any level of risk that exceeds an acceptable level, whetherthe acceptable level be predetermined or dynamically determined (e.g.,certain purchasers, merchants, regions, times of day, or the like mayhave differing acceptable levels of risk).

Based on the likelihood, the processor may authorize or deny the newtransactions. For example, the processor may authorize the newtransaction when the likelihood is below a threshold. If the processorrejects the new wavelet, the processor may send a notification to sucheffect. For example, the processor may send a rejection signal or amessage indicating the likelihood and/or a reason (e.g., based on theone or more models) for rejection. The processor may send thenotification to one or more parties associated with the new transaction(e.g., a financial institution, an individual, a merchant, or the like)and/or to one or more computer systems from which the new transactionwas received (e.g., a personal computer such as a desktop computer ormobile phone, a point-of-service system, a financial processing server,a credit bureau server, or the like).

In some embodiments, based on the likelihood, the processor may requestmanual verification of the new transaction. For example, if thelikelihood is above a first threshold but below a second threshold, theprocessor may send one or more messages to one or more partiesassociated with the new transaction (e.g., a financial institution, anindividual, a merchant, or the like) with a request to send confirmationof the new transaction. In such an example, the processor may send amessage to a mobile phone and/or email address of the individual torequest that the new transaction be verified (e.g., by sending a “Y,”“yes,” or other affirmative response). Additionally or alternatively,the processor may send a message to a merchant warning that a suspicioustransaction has been processed and that the merchant will be deniedfuture transactions if the number of suspicious transactions in a periodof time exceeds a threshold.

Turning now to FIG. 1, there is shown an example of a wavelet. Forexample, the wavelet is an oscillation with an amplitude rising fromzero to a maximum and returning to zero over a finite period of time. Asexplained above, systems of the present disclosure may encodetransactions as wavelets. For example, a transaction may be visualizedas a wavelet in which currency and/or commodity is temporarily disturbedby transfer between parties. The wavelet representing the transactionmay be indexed by location, time, category of transaction (e.g.,furniture, contractor services, grocery, or the like), and/or otherindicators.

FIG. 2A depicts an exemplary filter bank used to perform a discretewavelet transform. For example, as depicted in FIG. 2A, the cascadingfilters may decompose a signal into low and high frequencies at eachlevel and may produce corresponding coefficients. The decomposition (andcorresponding coefficients) may be output from a convolution at eachlevel that samples particular frequencies. A graphical depiction offrequency range for each level of the filters of FIG. 2A is depicted inFIG. 2B.

FIG. 3 depicts an exemplary convolutional-accumulator. The example ofFIG. 3 is systematic because is includes the input data in output W aswell as outputting convolution X. Although not depicted, non-systematicconvolutional-accumulators may be used in combination with or in lieu ofsystematic convolutional-accumulators. Furthermore, the example of FIG.3 is recursive because the convolutional output may be fed back into theconvolutional-accumulator for use in other convolutions. Although notdepicted, non-recursive convolutional-accumulators may be used incombination with or in lieu of recursive convolutional-accumulators.

Systems of the present disclosure may use cascadingconvolution-accumulators, similar to the examples depicted in FIGS. 2and 3, to perform discrete wavelet transforms and obtain a tensor fromthe accumulation. In some embodiments, the accumulation function may bean exponential smoothing average to incorporate the natural base e intothe tensor.

FIG. 4 depicts exemplary coefficients (depicted as columns in FIG. 4)used to perform exponential smoothing. As depicted in FIG. 4, thecoefficients may exponentially decrease as the number of observationsincluded in the smoothing linearly increases. Accordingly, as explainedabove, the natural base e is incorporated into the resulting smoothedtensor, which increases the ease of detecting anomalous tensors infinancial markets.

FIG. 5 depicts an exemplary transformation from discrete wavelets (S(Δt)as depicted in FIG. 5) to tensors. In particular, the discrete waveletsmay undergo convolution (e.g., recursively as depicted in FIG. 5)followed by one or more accumulating (and smoothing) operations(D(S_(m)) as depicted in FIG. 5). For example, D(S_(m)) may representany moving average, such as a simple moving average, a cumulative movingaverage, a weighted moving average, or the like. In some embodiments,D(S_(m)) may represent an exponential smoothing average, as explainedabove with reference to FIG. 4.

FIG. 6 depicts an exemplary manifold onto which a plurality of tensorsare mapped. For example, similarly to the example of FIG. 6, systems ofthe present disclosure may map a set of tensors to a differentiablemanifold, which is a topological manifold having a differentiablestructure. Additionally, similar to the example of FIG. 6, systems ofthe present disclosure may use a smooth manifold, which is adifferentiable manifold having derivatives of all orders that existacross the entire manifold. Additionally, similar to the example of FIG.6, systems of the present disclosure may use an analytic manifold, whichis a smooth manifold whose Taylor series is absolutely convergent.Additionally or alternatively, although not shown in FIG. 6, systems ofthe present disclosure may use a complex manifold, which is a manifoldin complex space that is holomorphic.

FIG. 7 depicts an exemplary atlas mapping a subset of points to pointson a manifold (such as that depicted in FIG. 6) by an index set. Byselecting an appropriate atlas to perform a mapping, various constraintson the resulting manifold may be obtained. For example, by selecting anappropriate atlas, systems of the present disclosure may ensure themapping of tensors onto a differentiable manifold (or a smooth manifold,an analytic manifold, a complex manifold, or the like).

FIG. 8 depicts an example Galois connection between a base field

and a group G={f,f²,g,gf,gf²}. As depicted in FIG. 8, three subgroups ofG and three subfields of

are isomorphic. Systems of the present disclosure may use a Galoisconnection between a field and a tensor (or group) to calculatedifference vectors while ensuring isomorphism between the field and thetensor.

FIG. 9 depicts an exemplary artificial neural network as used in extantsystems. In neural networks like the example depicted in FIG. 9, one ormore inputs (e.g., real numbers) are processed by nodes (or neurons) ina hidden layer in order to produce outputs. Although not depicted inFIG. 9, the hidden layer may comprise a plurality of layers such thatsome nodes pass their output(s) to an additional hidden layer ratherthan directing outputting. Each node (or neuron) typically has aweighting function (often non-linear), and its weights are modifiedduring a learning procedure to reduce a loss function (and thereforeincrease accuracy).

Unlike the Galois connection networks used by systems of the presentdisclosure, however, neural networks like that depicted in FIG. 9frequently fail to recognize particular patterns. In addition, there maybe significant numbers of false positives (and, correspondingly, falsenegatives) in the use of neural networks. Galois connection networksdeveloped according to the present disclosure generally produce higheraccuracy and, corresponding, lower false positives and false negativesthan traditional neural networks.

FIG. 10A depicts an exemplary system 1000 for detecting anomalies withina database comprising discrete wavelets. System 1000 may be implementedon one or more servers, such as detection server 1501 of FIG. 15. Theone or more servers may be housed on one or more server farms.

As depicted in FIG. 10A, system 1000 may use wavelets 1001 as input. Forexample, as explained above, wavelets 1001 may be received by system1000 (e.g., from one or more memories and/or over one or more computernetworks) and/or determined by system 1000 based on data (e.g., one ormore transactions) received by system 1000.

As further depicted in FIG. 10A, system 1000 may convert wavelets 1001to tensors 1003. For example, as explained above, system 1000 mayperform a discrete wavelet transform (that is, a cascading convolution)with a smoothing accumulator to transform the wavelets 1001 to tensors1003. In some embodiments, a simple moving average, a cumulative movingaverage, a weighted moving average, or the like, may be used forsmoothing. In certain aspects, the smoothing may be an exponentialsmoothing average. By using an exponential smoothing average, thenatural base e may be incorporated into the smoothing.

As further depicted in FIG. 10A, system 1000 may convert tensors 1003 toa field 1005. For example, as explained above, system 1000 may use oneor more atlases to map tensors 1003 onto a manifold to form field 1005.In some embodiments, system 1000 may select the one or more atlases toensure particular properties of the resulting manifold (e.g., to resultin a differential manifold, a smooth manifold, an analytic manifold, acomplex manifold, or the like).

Field 1005 may be used by system 1000 to detect anomalous wavelets, asexplained above. For example, system 1000 may calculate a differencefield between a new wavelet and field 1005 and may sum the differencefield to form a difference vector. Accordingly, the magnitude and/ordirection of the difference vector may be used to determine an anomalylikelihood (e.g., using one or more models, as explained above).

FIG. 10B depicts another exemplary system 1000′ for detecting anomalieswithin a database comprising discrete wavelets. System 1000′ may beimplemented on one or more servers, such as detection server 1501 ofFIG. 15. The one or more servers may be housed on one or more serverfarms.

Similar to system 1000 of FIG. 10A, system 1000′ receives wavelets 1001,converts wavelets 1001 to tensors 1003, and maps tensors 1003 to field1005. In addition, as depicted in FIG. 10B, system 1000′ determineswavelets 1001 based on received input comprising JavaScript ObjectNotation (JSON) data. Additional or alternative data serializationformats, such as Extensible Markup Language (XML), YAML Ain′t MarkupLanguage (YAML), or the like. Data serialization formats allow for rapidand lightweight transmission of data (e.g., transactions) to system1000′. In addition, data serialization formats may allow for direct useof the received data (e.g., for conversion to wavelets or even fordirect processing by a discrete wavelet transform) without having toreconstruct a data structure or object therefrom. Furthermore, manyextant database structures (such as MongoDB, Oracle NoSQL Database, orthe like) support native exportation directly to a data serializationformat such as JSON. Accordingly, accepting data serialization formatsmay allow for faster and more native integration with existingtransaction databases.

FIG. 100 depicts an exemplary workflow 1050 of detecting a high risktransaction using a database comprising discrete wavelets. For example,workflow 1050 may represent one exemplary usage of system 1000 of FIG.10A and/or system 1000′ of FIG. 10B.

At step 1051, system 1000 receives a new transaction. For example, asexplained above, system 1000 may receive a wavelet representing atransaction, may receive a data serialization format for use as thoughit were a wavelet, and/or raw data for conversion to a wavelet and/or adata serialization format.

At steps 1053 a and 1053 b, system 1000 may extract a first indicatorand a second indicator from the new transaction. For example, the firstindicator may comprise an identifier of a financial account, anidentifier of a merchant, a location of the new transaction, a time ofthe new transaction, an Internet Protocol (IP) address or otheridentifier of a payment device (e.g., a mobile phone) and/or of apoint-of-service system (e.g., a register), or the like. Similarly, thesecond indicator may comprise an identifier of a financial account, anidentifier of a merchant, a location of the new transaction, a time ofthe new transaction, an IP address or other identifier of a paymentdevice (e.g., a mobile phone) and/or of a point-of-service system (e.g.,a register), or the like.

In addition, at step 1055, system 1000 may convert the new transactionto a tensor, as explained above. For example, system 1000 may perform adiscrete wavelet transform (that is, a cascading convolution) with asmoothing accumulator to transform the new transaction to a tensor. Insome embodiments, a simple moving average, a cumulative moving average,a weighted moving average, or the like, may be used for smoothing. Incertain aspects, the smoothing may be an exponential smoothing average.By using an exponential smoothing average, the natural base e may beincorporated into the smoothing.

At steps 1057 a and 1057 b, system 1000 may use the first indicator andthe second indicator to generate wavelets from the new transactionindexed by and/or incorporating the properties of the first indicatorand the second indicator. In some embodiments, these wavelets may befurther converted to tensors, as explained above.

In addition, at step 1059, system 1000 may determine a differencebetween the new transaction tensor and an existing tensor database(e.g., a tensor field representing previous transaction tensors mappedto a manifold). For example, as explained above, system 1000 maydetermine a difference field between the new transaction tensor and theexisting tensor database and sum the difference field into a differencevector.

At steps 1061 a and 1061 b, system 1000 may use the wavelets indexed byand/or incorporated into the first indicator and the second indicator tofind matching wavelets in the existing tensor database. For example,system 1000 may determine whether the matching wavelets are in anexpected location in the database (e.g., in the field) in order toassist with authorizing the new transaction.

In addition, at step 1063, system 1000 may apply a model (or a pluralityof models) to the difference between the new transaction tensor and anexisting tensor database. For example, as explained above, system 1000may apply the model to determine a likelihood of the new transactionbeing anomalous (and/or high risk). In some embodiments, as depicted inFIG. 100, system 1000 may include the first indicator and the secondindicator as inputs to the model. For example, the first indicatorand/or the second indicator may server to select the model (or pluralityof models) to apply. In such an example, the selection of the model (orplurality of models) may depend on a particular financial account, aparticular merchant, a particular location of the new transaction, aparticular time of the new transaction, a particular IP address of apayment device (e.g., a mobile phone) and/or of a point-of-servicesystem (e.g., a register), or any combination thereof.

By using workflow 1050, systems of the present disclosure mayincorporate traditional rule-based authentication techniques (e.g.,using the first indicator and the second indicator) with the deep fieldnetworks disclosed herein. Accordingly, systems of the presentdisclosure may be used to combine extant transactions authorizationswith novel determinations of fraudulency likelihood.

Although FIG. 100 depicts using a first indicator and a secondindicator, workflow 1050 of FIG. 100 may incorporate any number ofindicators, such as one, two, three, four, five, or the like. Inalternative embodiments not depicted, workflow 1050 of FIG. 100 may usethe model (or plurality of models) without any additional indicators.

FIG. 10D depicts an exemplary workflow 1080 of constructing and using adatabase comprising discrete wavelets. For example, workflow 1080 mayrepresent an additional or alternative example usage of system 1000 ofFIG. 10A and/or system 1000′ of FIG. 10B.

As depicted in FIG. 10D, one or more sources of transactions for systemsof the present disclosure may include one or more data lakes comprisinga distributed file system (such as Apache Hadoop or the like), one ormore data lakes comprising images (such as Microsoft Azure Data Lake orthe like), one or more real-time online transaction processing systems(RT-OLTPS) (such as PayPal or the like), one or more data oceans (suchas JSON objects exchanged using a Representational State Transfer (REST)protocol, XML objects exchanged using a Simple Object Access Protocol(SOAP), or the like). Accordingly, system 1000 may receive historicaltransactions, transactions awaiting authorization, or a combinationthereof. Although depicted as using JSON objects, other dataserialization formats such as XML, YAML, or the like, may be used inlieu of or in combination with JSON objects.

As further depicted in FIG. 10D, Deep Decision may represent a systemaccording to the present disclosure (e.g., system 1000 of FIG. 10Aand/or system 1000′ of FIG. 10B). Accordingly, Deep Decision may usereceived transactions for training one or more models (e.g., accordingto method 1300 of FIG. 13, described below), for developing a tensorfield representing historical transactions (e.g., as described above),and/or for authorizing new, incoming transactions (e.g., according tomethod 1400 of FIG. 14, described below). Outputs from Deep Decision,which may include, for example, one or more trained models, one or morefields, and/or one or more authorizations, may be stored in one or morecaches, as depicted in FIG. 10D. Additionally or alternatively, outputsmay be send to other systems, such as a personal computer such as adesktop computer or mobile phone, a point-of-service system, a financialprocessing server, a credit bureau server, or the like.

FIG. 11 depicts an example of training a deep field network to detectanomalies within a database comprising discrete wavelets. Example 1100may represent a training sequence implemented on, for example, system1000 of FIG. 10A and/or system 1000′ of FIG. 10B.

As depicted in FIG. 11, transactions may be represented as one or morewavelets. Although depicted as two wavelets in FIG. 11, a transactionmay be represented with any number of wavelets (e.g., one, two, three,four, five, or the like). Additionally, although depicted as each havingtwo wavelets in FIG. 11, different transactions may be represented bydifferent numbers of wavelets. For example, a first transaction may berepresented by a single wavelet, and a second transaction may berepresented by three wavelets.

Furthermore, as depicted in FIG. 11, the wavelets may be converted totensors that have coefficients along selected bases. Although theexample of FIG. 11 includes three bases, any number of bases (e.g., one,two, three, four, five, or the like) may be used. In addition, thewavelets may be converted to a plurality of tensors, each havingdifferent coefficients along different bases.

As further depicted in FIG. 11, the tensors may be grouped based oncorresponding coefficients. In the example of FIG. 11, the tensorsrepresenting the first transaction are placed in a first group while thetensors representing the second transaction are placed in a secondgroup. Although depicted as grouped together in FIG. 11, tensorsrepresenting the same transaction may be placed in different groupsbased on having different coefficients (e.g., by having differentbases). The groups depicted in FIG. 11 may be used to perform trainingof one or more models for each group (e.g., as discussed with respect tomethod 1300 of FIG. 13).

FIG. 12 is a flowchart of exemplary method 1200 for detecting anomalieswithin a database comprising discrete wavelets. Method 1200 may beimplemented using a general-purpose computer including at least oneprocessor, e.g., detection server 1501 of FIG. 15. Alternatively, aspecial-purpose computer may be built for implementing method 1200 usingsuitable logic elements.

At step 1201, a processor may receive a new wavelet. Although theprocessor may receive the wavelet in the form of a wavelet, the waveletneed not be received in the form of an oscillation but may berepresented in any appropriate form (e.g., an array, a digital signal,or the like). The wavelet may be received from one or more memoriesand/or across one or more computer networks.

Alternatively, the processor may receive data and convert the data intoa wavelet. For example, the processor may receive a transaction havingassociated properties (such as time, location, merchant, amount, etc.)and may convert the transaction into a wavelet or into an array or otherformat that represents a wavelet. The data may be received in and/orconverted to one or more data serialization formats, such as JSON, XML,YAML, etc.

At step 1203, the processor may convert the wavelet to a tensor. Forexample, as explained above, the processor may convert the wavelet to atensor based using a moving average, such as a simple moving average, acumulative moving average, a weighted moving average, an exponentialmoving average, or the like. Accordingly, the processor may perform acascading convolution (e.g., with one or more filter banks) followed byan accumulation (e.g., using the moving average for smoothing) totransform the received wavelet into a tensor.

At step 1205, the processor may calculate a difference field between thetensor and a field having one or more previous wavelets represented astensors. For example, the processor may have previously calculated thefield using wavelets received in the past. Similarly to step 1203, theprocessor may perform cascading convolution (e.g., with one or morefilter banks) followed by an accumulation (e.g., using the movingaverage for smoothing) to transform the previous wavelets into tensorsand obtain the field by mapping the tensors onto a manifold (e.g., adifferential manifold or the like) using one or more atlases.

Alternatively, the processor may receive the tensors representing theprevious wavelets (e.g., from one or more memories and/or over one ormore computer networks) and construct the field therefrom.Alternatively, the processor may receive the field directly (e.g., fromone or more memories and/or over one or more computer networks).

At step 1207, the processor may perform a weighted summation of thedifference field to produce a difference vector. For example, thecoefficient weights may be derived from training of one or moreparticular models. The one or more models may be trained for particularidentifiers (e.g., particular accounts, particular persons, particularmerchants, particular institutions, etc.), particular times (e.g., timeof day, time of year, etc.), particular locations (e.g., particularcountry, particular city, particular postal code, etc.), or the like.Additionally or alternatively, as explained above, the summation mayinclude a notch filter.

At step 1209, the processor may apply one or more models to thedifference vector to determine a likelihood of the new waveletrepresenting an anomaly. As explained above, the likelihood may beoutput from one or more particular models. The one or more models may betrained for particular identifiers (e.g., particular accounts,particular persons, particular merchants, particular institutions,etc.), particular times (e.g., time of day, time of year, etc.),particular locations (e.g., particular country, particular city,particular postal code, etc.), or the like.

At step 1211, the processor may add the new wavelet to the field whenthe likelihood is below (or equal to) a threshold. Accordingly, theprocessor may accept the new wavelet as a valid historical datapoint tobe used in future anomaly detection.

Method 1200 may include additional steps. For example, method 1200 mayinclude sending a rejection signal or a message indicating thelikelihood and/or a reason (e.g., based on the one or more models) forrejection when the likelihood is above (or equal to) the threshold. Theprocessor may send the notification to one or more parties associatedwith the new wavelet (e.g., a financial institution, an individual, amerchant, or the like) and/or to one or more computer systems from whichthe new wavelet was received (e.g., a personal computer such as adesktop computer or mobile phone, a point-of-service system, a financialprocessing server, a credit bureau server, or the like). Similarly,method 1200 may include sending an acceptance signal or a messageindicating the likelihood and/or a reason (e.g., based on the one ormore models) for acceptance when the likelihood is below (or equal to)the threshold. The notification may be sent similarly to the rejectionsignal or message.

FIG. 13 is a flowchart of exemplary method 1300 for training a deepfield network to detect anomalies within a database comprising discretewavelets. Method 1300 may be implemented using a general-purposecomputer including at least one processor, e.g., detection server 1501of FIG. 15. Alternatively, a special-purpose computer may be built forimplementing method 1300 using suitable logic elements.

At step 1301, a processor may receive a plurality of transactions. Thetransactions need not be received in any particular format but may berepresented in any appropriate form such as arrays, digital signals, orthe like. The transactions may be received from one or more memoriesand/or across one or more computer networks. Alternatively, theprocessor may receive raw data and convert the data into a formatrepresenting a transaction. For example, the processor may receive adata with time, location, party identifiers, amount, and the like andmay convert this data into a single bundle representing a transaction.

At step 1303, the processor may convert each transaction to acorresponding wavelet. For example, as explained above, the processormay receive a transaction having associated properties (such as time,location, merchant, amount, etc.) and may convert the transaction (alongwith its associated properties) into a wavelet or into an array or otherformat that represents a wavelet. Additionally or alternatively, theprocessor may convert raw data representing a transaction to one or moredata serialization formats, such as JSON, XML, YAML, etc., that may beoperated on as though it were a wavelet.

At step 1305, the processor may group the plurality of wavelets andcorresponding tensors by coefficients included in the wavelets. Forexample, as explained above, the corresponding tensors may be determinedusing one or more convolutional-accumulators. Because each tensorincludes coefficients for each base in the set of bases representing acorresponding multi-dimensional space in which the tensor may berepresented, the processor may group the tensors (and therefore, thecorresponding wavelets) by these coefficients. In some embodiments, theprocessor may generate a plurality of groups of coefficients and, thus,a plurality of groupings of the tensors (with the correspondingwavelets). For example, the processor may select bases depending onwhich factors are most heavily weighted in one or more models beingtrained and then perform a plurality of groupings, each for a particularmodel (or set of models) having factors corresponding to the bases usedto determine the corresponding grouping.

At step 1307, the processor may train a neural network for each groupindependently of other groups. Although “neural network” usually refersto a traditional artificial neural network as depicted, for example, inFIG. 9, the processor at step 1307 may train any model (e.g., the modelsdiscussed above with respect to the groupings) that produces alikelihood of a particular tensor being anomalistic within a group. Asused herein, the term “train” refers to the adjustment of one or moreparameters of the model (such as coefficients, weights, constants, orthe like) to increase accuracy of the model (e.g., to match knownproperties of the tensors in the each group).

At step 1309, processor may integrate the neural networks into a deepfield network. For example, the models may be combined into a largerpredictive scheme. In one particular example, the models may be combinedsuch that when a new tensor is convolved (or otherwise combined with themodels), the model trained on the group (or groups) having the mostsimilar coefficients will be amplified while other models (e.g., trainedon groups with less similar coefficients) will be minimized.

Method 1300 may include additional steps. For example, the deep fieldnetwork produced by step 1309 may be stored (or transmitted for remotestorage) for use in future analysis. In addition, the processor mayindex the stored deep field network such as different models within thenetwork may be extracted using one or more indices indicating theproperties and/or coefficients on which the model was trained (and towhich the model is sensitive).

FIG. 14 is a flowchart of exemplary method 1400 for authorizing atransaction using cascading discrete wavelets. Method 1400 may beimplemented using a general-purpose computer including at least oneprocessor, e.g., detection server 1501 of FIG. 15. Alternatively, aspecial-purpose computer may be built for implementing method 1400 usingsuitable logic elements.

At step 1401, a processor may receive a new transaction. The newtransaction need not be received in any particular format but may berepresented in any appropriate form such as arrays, digital signals, orthe like. The new transaction may be received from one or more memoriesand/or across one or more computer networks. Alternatively, theprocessor may receive raw data and convert the data into a formatrepresenting a transaction. For example, the processor may receive adata with time, location, party identifiers, amount, and the like andmay convert this data into a single bundle representing a transaction.

At step 1403, the processor may convert the new transaction to awavelet. For example, as explained above, the processor may convert newthe transaction (along with its associated properties) into a wavelet orinto an array or other format that represents a wavelet. Additionally oralternatively, the processor may convert raw data representing the newtransaction to one or more data serialization formats, such as JSON,XML, YAML, etc., that may be operated on as though it were a wavelet.

At step 1405, the processor may convert the wavelet to a tensor using anexponential smoothing average. For example, as explained above, thecorresponding tensors may be determined using one or moreconvolutional-accumulators

At step 1407, the processor may calculate a difference field between thetensor and a field having one or more previous transactions representedas tensors. For example, the processor may have previously calculatedthe field using transactions received in the past. Similarly to step1405, the processor may perform cascading convolution (e.g., with one ormore filter banks) followed by an accumulation (e.g., using the movingaverage for smoothing) to transform the previous transactions intotensors and obtain the field by mapping the tensors onto a manifold(e.g., a differential manifold or the like) using one or more atlases.

Alternatively, the processor may receive the tensors representing theprevious transactions (e.g., from one or more memories and/or over oneor more computer networks) and construct the field therefrom.Alternatively, the processor may receive the field directly (e.g., fromone or more memories and/or over one or more computer networks).

At step 1409, the processor may perform a weighted summation of thedifference field to produce a difference vector. For example, thecoefficient weights may be derived from training of one or moreparticular models. The one or more models may be trained for particularidentifiers of transactions (e.g., particular financial accounts,particular persons, particular merchants, particular financialinstitutions, etc.), particular transaction times (e.g., time of day,time of year, etc.), particular transaction locations (e.g., particularcountry, particular city, particular postal code, etc.), or the like.Additionally or alternatively, as explained above, the summation mayinclude a notch filter.

At step 1411, the processor may apply one or more models to thedifference vector to determine a likelihood of the transaction beinghigh risk. As explained above, the likelihood may be output from one ormore particular models. The one or more models may be trained forparticular identifiers of transactions (e.g., particular financialaccounts, particular persons, particular merchants, particular financialinstitutions, etc.), particular transaction times (e.g., time of day,time of year, etc.), particular transaction locations (e.g., particularcountry, particular city, particular postal code, etc.), or the like.

At step 1413, the processor may authorize the new transaction when thelikelihood is below a threshold. Accordingly, the processor may acceptthe new wavelet as a valid historical datapoint to be used in futureanomaly detection.

Additionally or alternatively, the processor may use the likelihooddetermined at step 1412 to perform other functions. For example, if thenew transaction is enrollment of a new account (such as a brokerageaccount, a credit card account, or the like), the processor may use thelikelihood determined at step 1412 to set one or more parameters for theaccount. In such an example, the likelihood may be used to determine aninterest rate for the account, a margin requirement for the account, anoptions trading level for the account, or the like. In another example,if the new transaction is a brokerage trade, the processor may use thelikelihood determined at step 1412 for initializing settlement of thetrade. In yet another example, if the new transaction is a portfoliorebalancing, the processor may use the likelihood determined at step1412 for approving the rebalancing, adjusting the rebalancing, or thelike.

Method 1400 may include additional steps. For example, method 1400 mayincorporate traditional authorization in combination with step 1413. Inone example, method 1400 may include identifying one or more indicatorsfrom the new transaction and authorizing the new transaction when theone or more indicators match expected values. Additionally oralternatively, method 1400 may include identifying one or moreindicators from the new transaction, using the one or more indicators toidentify matching wavelets, and authorizing the new transaction when thematching wavelets are in expected locations in the field. Additionallyor alternatively, method 1400 may include identifying one or moreindicators from the new transaction and using the one or more indicatorsas inputs to the model(s) for determining the likelihood.

In another example, method 1400 may include requesting manualverification of the new transaction when the likelihood is above a firstthreshold but below a second threshold. For example, the processor maysend one or more messages to one or more parties associated with the newtransaction (e.g., a financial institution, an individual, a merchant,or the like) with a request to send confirmation of the new transaction.In such an example, the processor may send a message to a mobile phoneand/or email address of the individual to request that the newtransaction be verified (e.g., by sending a “Y,” “yes,” or otheraffirmative response). Additionally or alternatively, the processor maysend a message to a merchant warning that a suspicious transaction hasbeen processed and that the merchant will be denied future transactionsif the number of suspicious transactions in a period of time exceeds athreshold.

Additionally or alternatively, method 1400 may include sending arejection signal or a message indicating the likelihood and/or a reason(e.g., based on the one or more models) for rejection when thelikelihood is above (or equal to) the threshold. The processor may sendthe notification to one or more parties associated with the newtransaction (e.g., a financial institution, an individual, a merchant,or the like) and/or to one or more computer systems from which the newtransaction was received (e.g., a personal computer such as a desktopcomputer or mobile phone, a point-of-service system, a financialprocessing server, a credit bureau server, or the like). Similarly,method 1400 may include sending an acceptance signal or a messageindicating the likelihood and/or a reason (e.g., based on the one ormore models) for acceptance when the likelihood is below (or equal to)the threshold. The notification may be sent similarly to the rejectionsignal or message.

The disclosed systems and methods may be implemented on one or morecomputing devices. Such a computing device may be implemented in variousforms including, but not limited to, a client, a server, a networkdevice, a mobile device, a laptop computer, a desktop computer, aworkstation computer, a personal digital assistant, a blade server, amainframe computer, and other types of computers. The computing devicedescribed below and its components, including their connections,relationships, and functions, is meant to be an example only, and notmeant to limit implementations of the systems and methods described inthis specification. Other computing devices suitable for implementingthe disclosed systems and methods may have different components,including components with different connections, relationships, andfunctions.

As explained above, FIG. 15 is a block diagram that illustrates anexemplary detection server 1501 suitable for implementing the disclosedsystems and methods. Detection server 1501 may reside on a single serverfarm or may be distributed across a plurality of server farms.

As depicted in FIG. 15, detection server 1501 may include at least oneprocessor (e.g., processor 1503), at least one memory (e.g., memory1505), and at least one network interface controller (NIC) (e.g., NIC1507).

Processor 1503 may comprise a central processing unit (CPU), a graphicsprocessing unit (GPU), or other similar circuitry capable of performingone or more operations on a data stream. Processor 1503 may beconfigured to execute instructions that may, for example, be stored onmemory 1505.

Memory 1505 may be volatile memory (such as RAM or the like) ornon-volatile memory (such as flash memory, a hard disk drive, or thelike). As explained above, memory 1505 may store instructions forexecution by processor 903.

NIC 1507 may be configured to facilitate communication with detectionserver 1501 over at least one computing network (e.g., network 1509).Communication functions may thus be facilitated through one or moreNICs, which may be wireless and/or wired and may include an Ethernetport, radio frequency receivers and transmitters, and/or optical (e.g.,infrared) receivers and transmitters. The specific design andimplementation of the one or more NICs depend on the computing network1509 over which detection server 1501 is intended to operate. Forexample, in some embodiments, detection server 1501 may include one ormore wireless and/or wired NICs designed to operate over a GSM network,a GPRS network, an EDGE network, a Wi-Fi or WiMax network, and aBluetooth® network. Alternatively or concurrently, detection server 1501may include one or more wireless and/or wired NICs designed to operateover a TCP/IP network.

Processor 1503, memory 1505, and/or NIC 1507 may comprise separatecomponents or may be integrated in one or more integrated circuits. Thevarious components in detection server 1501 may be coupled by one ormore communication buses or signal lines (not shown).

As further depicted in FIG. 15, detection server 1501 may include amerchant interface 1511 configured to communicate with one or moremerchant servers (e.g., merchant server 1513). Although depicted asseparate in FIG. 15, merchant interface 1511 may, in whole or in part,be integrated with NIC 1507.

As depicted in FIG. 15, detection server 1501 may include and/or beoperably connected to a database 1515 and/or a storage device 1517.Database 1515 may represent a wavelet database or other digitaldatabase, which may be stored, in whole or in part, on detection server1501 and/or, in whole or in part, on a separate server (e.g., one ormore remote cloud storage servers). Storage device 1517 may be volatile(such as RAM or the like) or non-volatile (such as flash memory, a harddisk drive, or the like).

I/O module 1519 may enable communications between processor 1503 andmemory 1505, database 1515, and/or storage device 1517.

As depicted in FIG. 15, memory 1505 may store one or more programs 1521.For example, programs 1521 may include one or more server applications1523, such as applications that facilitate graphic user interfaceprocessing, facilitate communications sessions using NIC 1507,facilitate exchanges with merchant server 1513, or the like. By way offurther example, programs 1521 may include an operating system 1525,such as DRAWIN, RTXC, LINUX, iOS, UNIX, OS X, WINDOWS, or an embeddedoperating system such as VXWorkS. Operating system 1525 may includeinstructions for handling basic system services and for performinghardware dependent tasks. In some implementations, operating system 1525may comprise a kernel (e.g., UNIX kernel). Memory 1505 may further storedata 1527, which may be computed results from one or more programs 1521,data received from NIC 1507, data retrieved from database 1515 and/orstorage device 1517, and/or the like.

Each of the above identified instructions and applications maycorrespond to a set of instructions for performing one or more functionsdescribed above. These instructions need not be implemented as separatesoftware programs, procedures, or modules. Memory 1505 may includeadditional instructions or fewer instructions. Furthermore, variousfunctions of detection server 1501 may be implemented in hardware and/orin software, including in one or more signal processing and/orapplication specific integrated circuits.

The foregoing description has been presented for purposes ofillustration. It is not exhaustive and is not limited to precise formsor embodiments disclosed. Modifications and adaptations of theembodiments will be apparent from consideration of the specification andpractice of the disclosed embodiments. For example, the describedimplementations include hardware and software, but systems and methodsconsistent with the present disclosure can be implemented with hardwarealone. In addition, while certain components have been described asbeing coupled to one another, such components may be integrated with oneanother or distributed in any suitable fashion.

Moreover, while illustrative embodiments have been described herein, thescope includes any and all embodiments having equivalent elements,modifications, omissions, combinations (e.g., of aspects across variousembodiments), adaptations and/or alterations based on the presentdisclosure. The elements in the claims are to be interpreted broadlybased on the language employed in the claims and not limited to examplesdescribed in the present specification or during the prosecution of theapplication, which examples are to be construed as nonexclusive.

Instructions or operational steps stored by a computer-readable mediummay be in the form of computer programs, program modules, or codes. Asdescribed herein, computer programs, program modules, and code based onthe written description of this specification, such as those used by theprocessor, are readily within the purview of a software developer. Thecomputer programs, program modules, or code can be created using avariety of programming techniques. For example, they can be designed inor by means of Java, C, C++, assembly language, or any such programminglanguages. One or more of such programs, modules, or code can beintegrated into a device system or existing communications software. Theprograms, modules, or code can also be implemented or replicated asfirmware or circuit logic.

The features and advantages of the disclosure are apparent from thedetailed specification, and thus, it is intended that the appendedclaims cover all systems and methods falling within the true spirit andscope of the disclosure. As used herein, the indefinite articles “a” and“an” mean “one or more.” Similarly, the use of a plural term does notnecessarily denote a plurality unless it is unambiguous in the givencontext. Words such as “and” or “or” mean “and/or” unless specificallydirected otherwise. Further, since numerous modifications and variationswill readily occur from studying the present disclosure, it is notdesired to limit the disclosure to the exact construction and operationillustrated and described, and accordingly, all suitable modificationsand equivalents may be resorted to, falling within the scope of thedisclosure.

Other embodiments will be apparent from consideration of thespecification and practice of the embodiments disclosed herein. It isintended that the specification and examples be considered as exampleonly, with a true scope and spirit of the disclosed embodiments beingindicated by the following claims.

What is claimed is:
 1. A system for detecting anomalies between newwavelets and fields of previous wavelets, the system comprising: one ormore memories storing instructions; and one or more processorsconfigured to execute the instructions to: receive a new wavelet,convert the wavelet to a tensor using an exponential smoothing average,calculate a difference field between the tensor and a field having oneor more previous wavelets represented as tensors, perform a weightedsummation of the difference field to produce a difference vector, applyone or more models to the difference vector to determine a likelihood ofthe new wavelet representing an anomaly, and add the new wavelet to thefield when the likelihood is below a threshold.
 2. The system of claim1, wherein at least one of the one or more models is specific to atleast one of a particular identifier, a particular location, and aparticular time of day.
 3. The system of claim 1, wherein converting thewavelet to a tensor includes applying a discrete wavelet transform. 4.The system of claim 3, wherein the discrete wavelet transform includes afilter bank comprising a plurality of convolutional-accumulators.
 5. Thesystem of claim 4, wherein the convolutional accumulators are configuredto accumulate using base e.
 6. The system of claim 4, wherein thediscrete wavelet transform includes the exponential smoothing average inthe filter bank.
 7. The system of claim 1, wherein the one or moremodels comprise a plurality of neural networks integrated into a deepfield network.
 8. The system of claim 1, wherein the threshold ispredetermined.
 9. The system of claim 1, wherein the threshold isdynamically determined based on the one or more models.
 10. The systemof claim 1, wherein the one or more models are selected based oncoefficients included in the tensor.
 11. The system of claim 1, whereinthe likelihood is determined based on a magnitude of the differencevector and a direction of the difference vector.
 12. The system of claim1, wherein the one or more processors are further configured to receivedata and convert the data into the new wavelet.
 13. The system of claim1, wherein the difference field comprises a tensor product of fields.14. The system of claim 13, wherein the tensor product is applied to afield including only the tensor and the field having one or moreprevious wavelets represented as tensors.
 15. The system of claim 1,wherein the one or more processors use one or more atlases to obtain thefield having one or more previous wavelets represented as tensors. 16.The system of claim 15, wherein the one or more atlases map the one ormore previous wavelets represented as tensors onto a manifold.
 17. Thesystem of claim 1, wherein the difference field comprises a Galoisconnection between the tensor and the field having one or more previouswavelets represented as tensors.
 18. The system of claim 1, wherein theone or more processors use a notch filter when performing the weightedsummation.
 19. The system of claim 18, wherein the notch filter isconfigured to filter one or more frequencies.
 20. The system of claim19, wherein the one or more frequencies are selected using the one ormore models.